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Integration Sum Help

Evaluate

\[ \Large{\sum _{ n=1,3,5,7.... }^{ \infty }{ \frac { { e }^{ \left( 2n-1 \right) } }{ \int _{ 0 }^{ n+1 }{ \frac { { x }^{ e }{ e }^{ x } }{ \left( x+1 \right) ! } dx } } } }\]

Note by Lakshya Sinha
11 months, 2 weeks ago

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@Jonas Katona Lakshya Sinha · 11 months, 2 weeks ago

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I'm currently busy now. Ty using the infinite product of gamma(x+2) Aditya Kumar · 11 months, 2 weeks ago

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What have you tried? What makes you think there's a closed form? Pi Han Goh · 11 months, 2 weeks ago

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@Pi Han Goh I don't know I just made this problem and asked my school teacher, she said it was pretty tough. So I asked for help. Lakshya Sinha · 11 months, 2 weeks ago

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@Lakshya Sinha Not all series /integrals has a nice closed form. Pi Han Goh · 11 months, 2 weeks ago

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@Pi Han Goh try this Lakshya Sinha · 11 months, 2 weeks ago

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@Lakshya Sinha See the report. Your problem is flawed. Pi Han Goh · 11 months, 2 weeks ago

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@Pi Han Goh Sorry Lakshya Sinha · 11 months, 2 weeks ago

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@Lakshya Sinha @Jake Lai Lakshya Sinha · 11 months, 2 weeks ago

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@Lakshya Sinha Very unlikely this series has a closed form. Factorials/gamma functions in integrals, especially in denominators of integrals, are difficult to evaluate in general.

It is best to proceed in the direction of a motivating problem which applies integration in its solution, or to build a problem on the back of techniques already well-studied. Jake Lai · 11 months, 2 weeks ago

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@Jake Lai I made it accidently Lakshya Sinha · 11 months, 2 weeks ago

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@Lakshya Sinha @Pi Han Goh Lakshya Sinha · 11 months, 2 weeks ago

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